Find Integer Solutions for (A+3B)(5B+7C)(9C+11A)=1357911

  • Context: MHB 
  • Thread starter Thread starter anemone
  • Start date Start date
  • Tags Tags
    Integer
Click For Summary
SUMMARY

The forum discussion focuses on finding integer solutions for the equation \((A+3B)(5B+7C)(9C+11A)=1357911\). The primary approach involves determining the prime factors of 1357911, which are five in total, and subsequently forming all possible groups of three factors. This method is essential for identifying potential integer combinations that satisfy the equation.

PREREQUISITES
  • Understanding of integer factorization
  • Familiarity with algebraic expressions and equations
  • Knowledge of prime numbers and their properties
  • Basic skills in combinatorial mathematics
NEXT STEPS
  • Research prime factorization techniques for large integers
  • Explore combinatorial methods for grouping factors
  • Learn about algebraic manipulation of polynomial equations
  • Investigate integer solution methods for multi-variable equations
USEFUL FOR

Mathematicians, students studying algebra, and anyone interested in solving complex integer equations.

anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
Find all integer solutions (if any) for the equation $(A+3B)(5B+7C)(9C+11A)=1357911$.
 
Mathematics news on Phys.org
I would start by finding the prime factors of 1375911 (there are five) then forming all groups of 3 factors.
 
Hi HallsofIvy!

Thanks for your reply. But since this is a challenge question, I hope you know our expectation here is to receive a full solution, no more, no less. (Happy)
 
No solution because

RHS is odd so all factors are odd so each term in the LHS is odd. there are 3 terms on the LHS and so their sum has to be odd.

but sum is 12A + 8B + 16C which is even so impossible
 

Similar threads

MHB Algebraic Rational Expressions
  • · Replies 5 ·
Replies
5
Views
2K
MHB Determine all pairs of integers
  • · Replies 5 ·
Replies
5
Views
2K
MHB Positive Integer Solutions of $(x^2+y^2)^n=(xy)^{2014}$
  • · Replies 2 ·
Replies
2
Views
2K
MHB Solve for positive integer solutions
  • · Replies 3 ·
Replies
3
Views
1K
MHB What are the solutions for (a,b) if 5a^2+5ab+5b^2=7a+14b?
  • · Replies 7 ·
Replies
7
Views
2K
High School How to find an integer solution to a nonlinear equation?
  • · Replies 6 ·
Replies
6
Views
2K
Use the Euclidean algorithm to find integers ## a, b, c ##
  • · Replies 5 ·
Replies
5
Views
1K
MHB Integer solutions of system of equations
  • · Replies 5 ·
Replies
5
Views
2K
MHB Integer Solutions for $4x+y+4\sqrt{xy}-28\sqrt{x}-14\sqrt{y}+48=0$
  • · Replies 1 ·
Replies
1
Views
1K
MHB Solving Integer Equations with $a$ and $b$
  • · Replies 4 ·
Replies
4
Views
1K